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U. S. Department of Commerce Research Paper RP2043 National Bureau of Standards Volume 43, December 1949 Part of the Journal of Research of the National Bureau of Standards

Dissociation Constants of Weak Bases from Electromotive-Force Measurements of of Partially Hydrolyzed

By Roger G. Bates and Gladys D. Pinching

A method for the determination of constants of weak by electromotive-force measurements of solutions of partially hydrolyzed salts of a weak and a weak is described. Although the precision is only half that of the conventional emf method, this procedure has particular advantage in determining t he dissociation constants of certain bases, for some of the experimental difficul ties encountered in adapting the usual method to solutions containing these bases can be overcome or red uced. The - concentration of a of a of this type depends upon the constants of the weak acid, th e , and . If two of these are known, the third can be evaluated by means of e mf meas urements wi t hout the necessity of knowing the exact hydrogen-ion concentration, which is usually difficult to obtain. Hydrogen clectrodes and silver-silver electrodes are used in the cells, and the solutions are aqueous mixtures containing the of the sa lt and an chloride. The equations for t he calculation of dissociation constants are developed. The method was tested by a determination of the

basic of tris(hydroxymethyl)aminomcthane at 20 0 , 25 0 , and 30 0 C from three se ri es of measu remen ts : (a) by t he con ventional em f method ; (b) by emf studies of the of mixtures of the a mine and primary ; and (c) by emf studies of the hydrolysis of mixtures of the and potassium p-phenolsulfonate. The three determinations were in acceptable agreement. The negative logarithm of the hasic

dissociation constant, Pf(b, was found to be 5.946 at 20 0 , 5.920 at 25 0 , and 5.896 at 30 0 C.

1. Introduction and for the of silver chloride but must Although the experimental difficulties met in the retard the diffusion of silver to the hydrogen study of most weak bases are not insurmountable, electrode as well. they have been in large part responsible for the Replacement of the silver-silver chloride elec­ failure of this important class of substances to trode by a type less susceptible to reaction with receive the attention it deserves. The hydrogen­ bases has been suggested [5, 6], but some silver chloride cell, so useful in precise determina­ sacrifice of reproducibility may be expected [7]. tions of the dissociation constants of weak Furthermore, it is desirable in the interest of by the electromotive-force method [1, 2, 3]1 ean consistency that dissociation constants of bases be successfully applied to a measurement of the should relate to the same cell used extensively in constant of ammonia only under special condi­ studies of weak acids and in measuring the ioniza­ tions [4]. Thus, if equimolal mixtures of ammonia tion constant of water. Nevertheless, the extra­ and chloride are to be investigated by polation to infinite dilution to obtain the thermo­ this method, one must not only determine and dynamic constant of a mono acidic base entails a apply corrections for the volatility of ammonia greater uncertainty than for a monobasic acid, where the activity-coefficient term is practically 1 Figures in brackets indicate the literature references at tbe end of tbis paper. zero, or at worst a linear function of ionic strength. Dissociation Constants of Bases 519 859368- 49--2 It is well known that the pH of an aqueous term is usually small and the extrapolation to zero solution of a salt of" two-sided weakness", that is, salt concentration is easily effected. a salt formed by neutralization of a weak acid The solutions needed to determine the dissocia­ with a weak base, is fixed by the concentration tion constant of a weak base by the emf-hydrolysis and by the dissociation constants of the acid, the method are usually not difficult to prepare. If the base, and water. These three constants are desig­ free base is a solid and is readily obtained in the

nated by the symbols K a, K b , and K w, respectively. pure state, it is weighed and combined in solution Unfortunately, the pH cannot be uniquely de­ with an equivalent amount of the weak acid and termined [81. However, these dissociation con­ the desired amount of alkali chloride. If the acid stants can be expressed in terms of the measured is not a solid , and if the weak base is most con­ electromotive force of galvanic cells composed of veniently added in the form of its hydrochloride, hydrogen and silver-silver chloride electrodes im­ the solutions are made from equivalent amounts mersed in solutions of the weak salt with added of base hydrochloride and an of the chloride. The value of KaKw /Kb can be obtained weak acid_ by a suitable extrapolation to zero concentration The chief disadvantage of this method results of salt ions. A knowledge of the hydrogen-ion from the dependence of the emf of the cell upon concentration or activity is then unnecessary. the geometric mean of two constants, that is upon

The extent of hydrolysis of the salt depends upon .../Ka(Kw/K b) , instead of upon K,,/Kb alone, as in the relative magnitudes of Ka and Kw/K~. For the usual emf method. Consequently the precision best results, the acid and base should be of such of determining Kb with the aid of known values strengths that at least 5 percent of each of the of K w and Ka is reduced by one-half. two salt ions is hydrolyzed, thus assuring an Tris(hydroxymethyl)aminomethane was chosen adequate buffer capacity. Similarly, degrees of for a comparison of the new procedure with the hydrolysis greater than 95 percent should be earlier method. This primary amine can be ob­ avoided. In general, this restriction means that tained as a pure solid readily soluble in water and log Ka and log (Kw /Kb ) should differ by no not appreciably volatile. It does not react with more than 2. silver ion so extensively as to prohibit the use of the This emf-hydrolysis method is often better silver-silver chloride in equimolal mixtures of the suited to the determination of the dissociation amine and its hydrochloride. E lectromotive-force constants of weak bases than is the conventional measurements were made at 20°, 25°, and 30° C emf method. The low buffer capacity near the on solutions of partially hydrolyzed salts of this ends of the pH-neutralization curve and the amine with primary phosphate ion (H2P04 - ) and difficul ty of evaluating the buffer ratio precisely wi th p -phenolsulfonate ion (HOC6H 4SOa- ), and the in these regions usually restrict the application of dissociation constant of the base was calculated the conventional method to solutions with buffer from the results. Thc constant was also found by ratios between 0.2 and 5. Nevertheless, a low the customary emf method [1 , 3]. The three ratio of free base to salt is sometimes desired in determinations were in acceptable agreement. order to minimize losses by volatilization and II. Description of the Method errors caused by the high solubility of silver chloride in the cell solutions. If Ka for the acid If the standard potential, EO, is known, each selected is larger than K w/Kb' less than half of the emf measurement of the hydrogen-silver chloride base ion will usually be transformed into free base, cell yields a value of - log (fHjCImH), where m is and these errors may be of little or no consequence. molality, j is the activity coefficient on the molal Under these conditions the buffer ratio may depart scale. and H designates the total hydrogen-ion widely from unity, but this disadvantage is offset species, hydrated or otherwise. This quantity by the double buffering action offered by the two has been called pwH for convenience and to sug­ systems set up by the incomplete reaction of the gest its status as a practical unit of acidity sus­ salt ions with water. Furthermore, the buffer ceptible of exact definition [8]. The pwH is ratio need not be established with great accuracy. calculated from the emf E by If the free base is uncharged and the acid chosen (E-EO) F is a singly charged anion, the activity-coefficient pwH= - log (fHjClmH) = 2.3026 RT+log mCl , (1)

520 Journal of Research where F , R, and Tare respecLively Lhe faraday, base, and eq 3b will also show little tendency to gas constant, and tempera ture on the Kelvin take place. However, when both BH+ and A ~ scale. The values of E O and 2.3026 RT/F are are parL of the same aqueous system, the everal summarized in another publication [4]. Thermo­ acids and bases present interact, and hydrolysis dynamic dissociation constants are derived from is no longer dependent solely upon the acidic and experimental values of pwH by expression of mrr ba ic . For example, BH+ 01' frrmrr in terms of the constants that fix their will be hydrolyzed to a larger extent in the pres­ values in the cell solutions, and extrapolation of ence of A = than by water alone, if A = is a stronger a suitable function of the dissociation constants base than water. The of BH+ has to zero concentration where the activity coeffi­ a similar influence upon the extent to which eq 3b cients become unity. proceeds. This behavior is quite adequately Three equilibria are of signifi cance in determin­ explained by eq 3a and 3b, for the concentrations ing the hydrogen-ion concentration in a solution of and hydroxyl ions cannot be varied of a salt of a weak acid anion, HA-, and weak independently in the same solution. monoacidic base, B.2 These arc the acidi c disso­ By combination of eq 3a with 3b, one can write sociation of the weak acid, the complete equation for the simultaneous hydrolysis of the ions BlF a nd A= :

BH++A=+2H20 = the basic dissociation of the weal,;: base, B + HA-+H 30 ++OH-; K~/Ka Kb ' (4)

It is clear th at Lhe two ions will not usually hy­ drolyze to equal exten ts, for K a and K b (and con­ and the ionization of water, sequ ently th e constants of eq 3a and 3b) will ordinarily be different. H ence, it is incorrect to apply the term "degree of hydrolysis" to a sal t of The equilibria among water and the salt ions a weak acid and a weak base. It should rather BH+ and A ~ arc expressed in Lcrms of the three be applied to each of the sal t ions individually. above: If K a and K b were indeed equal, and Lhus the degrees of hydrolysis of the individual ions as well, hydronium and hydroxyl ions would be produced and in equal numbers upon dissolving Lhe salt in water, as equilibrium 4 ind ica. Les; and the soluLion would r emain neuLra1 , or substan tially 0, at all concen­

In terms of the Br ~ n ste d-Lowl'y theory of acids trations. The inequality of K a and K b nOL only causes Lhe solution to be acid ic or alkaline but I and bases [9 , 10], eq 3a represents the acidic dis­ sociation of BH+, the of the base also gives rise to a change of pH wiLh concentra­ B , and eq 3b represents the dissociation of the tion [ll]. (hydrated) anion A ~ as a bast). Evidently the In order to calculate mrr or fumH in a solu tion of extent to which the separate reactions 3a and 3b this type, the fraction of BI-r+ hydrolyzed will be proceed to establish equilibrium is largely depend- designated aI, and the corresponding degree of hydrolysis of th e acid anion = will be called a2· i ent upon th e acidic and basic strengths of BH+ A and A = in comparison with the amphiprotic Hence, from the mass-law expression for equilib­ . If B is a rather trong base (and its rium 3a one can write l - al f NH/ conjugate acid BH+ cOl'l'espondingly weak), the - log K bh =-logfHmn+ log - + log -f - ' hydrolysis of BH+ by eq 3a will proceed but al N H 3 slightly unless one of the products, (5a) or free base, is removed. Similarly, if HA- is a and from eq 2a stronger acid than is water, A ~ will be a weak 1 T.T 1 f' 1 a2 1 .IHA - - og D.· a= - og Hmrr + og l - a ~ + og .I A - • 2 'rho equations can be derived in a similar mallJ1 Cl' for ac id s and bases of other electric types. (5b)

Dissociation Constants of Bases 521 These equations, together with that for the water lality m, is taken as 4m. Then a more accurate equilibrium, regulate the hydrogen-ion concentra­ value is obtained by tion. By combination of eq 1, 5a, and 5b we obtain M= 4m-m(3a2 + al)/2+ (mH+mOH) /2 "'-'4m(1-az/2). (\1)

- log ';KbhKa = pwH+ The simpler expression for M given in the last part of eq 9 is adequate when pwH is between 4 and 10. (6) With a2 from eq 8 and mn or mon (depending upon whether the solution is acidic or alkaline) calcu­ As usual,. pK= - log K. The analogy with the lated from pwH by equations for the product of the constants for overlapping successive dissociation steps of poly­ - log mn = pwH- 2A-./p..; (10) basic acids [12] is evident. l + Ba* p, and (11) 1. Calculation of the a Term From a consideration of eq 3a and 3b, the rela­ al can be obtained by eq 7a or 7b, and the second tionship between al and a2 can be derived. Hy­ term on the right of eq 6 can be evaluated. This dronium ion and hydroxyl ion are produced by term is quite small if a2 exceeds 0.1 and the pH these reactions in the molal amounts aim and lies between 4 and 10. It is less than 0.0001 for a2m, respectively, where m is again the stoichio­ equimolal mixtures of tris(hydroxymethyl)amino­ metric molality of each of the ions of the salt, and primary potassium phosphate at 20 0 usually not less than 0.01. By reaction with the to 30° C when m is 0.01 or greater. For a corre­ other ion, either hydronium or hydroxyl is reduced sponding mixture of the amine and potassium to a negligible concentration. If the salt solution p-phenolsulfonate, it amounts to 0.0004 at m= is neutral, al"'" a2. If acidic, 0.01. 2. The Extrapolation (7a) If the Debye-Huckel relation between ionic If alkaline, charge and activity coefficient were valid for these mixtures, the last term of eq 6 would be zero. The (7b) data presented in a later section indicate that this In the determination of basic dissociation con­ is not the case for equal molal mixtures of tris stants, an acid of known dissociation is selected. (hydroAJ'methyl)aminomethane, potassium dihy­ Equation 5b can be converted to a form convenient drogen phosphate (or potassium p-phenolsul­ for calculating a2: fonate), and potassium chloride. The last term of eq 6 can be divided into two 1-a2 2A ~ parts. The first, fBH +fcl-/fB, pertains to the base, 10g --"," pwH- pKa+ -yp" (8) a2 l + Ba*{";. and the second, jHA-fcdfA-, to the weak acid. It has been found that an activity-coefficient term where A and B are constants of the Debye­ of the first type (where B is NH3) can be repre- I Huckel theory [1 3], p, is the ionic strength, and sen ted satisfactorily by a* is an adjustable parameter whose value usually lies between 0 and 10. An average value, for A ·l;' (12) example 4, suffices for the purpose. It is desirable that a2 should not be much less than 0.1. Hence where (31 is a second parameter [4]. Likewise, the pwH should not be more than about 1 unit greater term for the acid system can be expressed simi­ than pKa. larly, as studies of the phosphate and phenolsul­ An approximate a2 with which to evaluate the fonate buffers [14 , 15] have shown. ionic strength is obtained from eq 7. For the first approximation, the ionic strength of mixtures of (13) base, acid, and potassium chloride, each at mo-

522 Journal of Research If at and a2 were equal, the last term of eq 6 would Two samples, titrated with a standard solution of b e a linear function of ionic strength. That it , required amounts of acid was not found to be so suggests that a t differs equivalent to 100.02 percent of the base. A mix­ frOln az. 3 ture of bromcresol green and ali zarin red S was It is desired simply to find an empirical expres­ used as indicator for one sample (see footnote 4) sion that will reduce the last term of eq 6 to a and the salt of methyl red for the other. lineal' function of ionic strength and h ence facil­ Color standards, adjusted to pH 4.8, the theoreti­ itate the extrapolation to Z0ro concentration. cal end-point in 0.05-M solution compu ted from From eq 12 and 13, the dissociation constant found by Glasstone and Schram [16], were used. The solubility of freshly AB(at - az}p 7~ 10 gjB H +jH A -j ~ t - +/3' precipitated silver chloride in two solu tions of the (1 + Bal ..ji;,) (1 + Baz..ji;,) j BjA- ~ amine was determined at room temperature. A A B (al-a2) /L (14) O.l -M solution of the amine dissolved 0.0021 mole ~ ( 1 + Ba ~ /L )2' of silver chloride per liter, and a O.l-M solu tion that was also 0.01 M with respec t to potassium where a is (at+az)/2, and /3' is the slope of a plot chloride dissolved 0.0007 mole. H ence, the solu­ of the left (or extr eme righ t) side of eq 14 as a bility of silver chloride is consider ably less than function of p. The approximate form (extreme in solutions of ammonia, and it is safe to conclude right of eq 14) was found to yield a satisfactory that no correction is necessary for the solubility straight line and was somewhat easier to compute in eq uimolal solu tions of tbe amine and its than the exact left-hand term. The value of /3' hydrochloride. differs, of course, with the form of equation chosen. " Apparent" values of the me ail of pRbh and The potassium dihydrogen phosphate was NBS Standard Sample 186 I. P otassium p­ pKa, namely [(pK IJh + pRa)/2j', are therefore com­ puted by eq 6 for various values of aJ and a2 with phenolsulfonate was dccolorized and then crystal­ ionic strengths established as described in the lized four times. The last crystallization was foregoing section. These values are plot ted as a from freshly boiled co nductivity water . The function of /L , and the shape of the curve is exam­ salt was dried a t 90° to 110° C. The pH of the ined . If necessary, a is varied until a straight O.l-M solutions was found by glass-electrode line results. It is eviden t that a[-aZ in the measuremen t to be abou t 5.1. This is close to numerator of eq 14 can be adjusted to alter th e the inflection point. The potassium chloride slope of the extrapolation plot if desired without had been purified by treatment wi th , affecting its curvatme, so long a.s a r ema ins un­ precipitation with gaseous , and changed . At zero ionic strength th e activity­ fusion [17] . H ydrochloric acid was distilled and coefficient term is zero, and the inter cep t is the the middle fraction collected and diluted to about true mean of the thermodynamic constants, H 0.1 M . Five sep arate determinations of the con­ centration of this standard solution by weighing (pKbh+pKa). Inasmuch as pKbh = pKw-pKb , and both K a and ](w are known, the basic constant silver chloride gave a mean deviation from the is readily obtained. mean of less than 0.02 p ercent. For the mixtures of amine and weak acid, the III. Experimental Procedures cell vessels were of the type ordinarily used for Purified tris(hydroxymethyl) aminomethane was studies of weak-acid systems [1 8], that is, with a obtained through the courtesy of Commercial single saturator and no stopcock between the Corporation. The commercial grade of electrode compartments. Those employed pre­ amine had been decolorized and crystallized t hree viously in the inves tigation of ammonia solutions times from a mixture of methanol and water .4 [4] were used for mixtures of amine and hydro­ . In view of the low volatility of the 3 Actually a, for the ammonia system was found to be abou t 2 14J, and valu es of 4.4 and 8 for a, were fo und for phos pbate and phenolsulfonate bufTer amine, however , the presaturator was not required. solutions [14, 15J . However, it wo uld be surprising if the parameters reo Ail' was removed from the solutions by passage of mained uncbanged in these solutions of partiall y hydrolyzed salts. , Comm unication from John A. Riddick. before the final weighing.

Dissociation Constants of Bases 523 IV. Results TABLE 2. Electromotive force of hydrogen-silver chloride cells containing solutions of tris(hydroxymethyl) amino­ The electromotive force of cells with hydrogen methane (m l) and its hydrochloride (m2) electrodes and silver-silver chloride electrodes and containing equimolal mixtures of tris(hydroxy­ Electromotive fo rce at- methyl)aminomethane, potassillm dihydrogen phos­ m, 20 ° 0- 0 30° phate (or potassium p-phenolsulfonate), and potas­ I -" I sium chloride is listed in table 1. The emf has ml =m2 been corrected in the usual manner to a of 1 atm of hydrogen. Table 2 gives the 0.08814 0.77789 0. 77594 O. 77376 . 07097 .78240 . 78050 . 77838 electromotive force of the same cell containing 15 . 05099 . 78940 .78757 . 78557 aqucous mixtures of tris(hydroxymethyl) amino­ . 02996 .80092 .79923 .79741 .02564 .80436 . 80266 .80099 methane and its hydrochloride. These data were . 01 5268 . 81585 .81432 .81283 obtained in order that the constan t of the amine . 009962 .82541 .82414 .82273 .009785 .82593 .82455 .82329 might be evaluated by the earlier or "convention­ .006092 . 83669 . 83560 .83445 al" method to furnish a test of the newer method . 003924 .84667 .84574 . 84477 based upon emf studies of partially hydrolyzed salts. I 71l1=0.3630 71l,

0. 09959 0.74998 0. 74738 0. 74474 T A BLE 1. Electmmotive f01'ce of hydrogen-silver chloride .07933 .75472 .75220 . 74960 cells containing solutions of tTis(hydroxymethyl) amino­ .05982 . 76066 .75819 . 75569 methane, weak acid, and potas, ium chloride, each at . 03974 . 76931 .76694 . 76458 molality m . 02024 . 78415 .78201 . 77985

Electromot ive for ce at- m data given in table 2 is also listed in the last col­ 20 ° I 25° I 30° umn. The following equation was used: AMINE+POTASSLUM DIHYDROGEN P HOSPHATE - log K':== - log K oh - {3m2= pwH+

0. 08038 0.73985 0. 74098 0.74189 100' m2 _ 2A-v'hl; . (15) . 05526 . 74892 . 75019 . 75124 b m l 1+ Ba*-v'm2 .03555 .75980 .76106 .76230 . 02025 . 77369 . 77524 . 77678 .011629 .78737 .78915 . 79085 TABLE 3. Values of 1/2 (pKbh+pK a) and pKbh derived from three seTies of emf measurements AMINE+POTASSIUM p-PHENOLSULFONATE

Acid 0.08111 0. 79604 0.79687 0. 79761 . 05667 .80452 .80546 . 80637 . 03622 . 81525 . 81634 . 81741 . 019945 . 82968 .83104 .83240 .010458 .84545 . 84705 . 84863 KH,PO. ______7. 7175± 0. 0006 8. 2220±O. 0012 KH Phenolslllfonate ______8. 6630±. 0002 8. 221O±. 0004 H OL ______8. 2214±. 0009 Table 3 lists th e mean of pKbh and pKa calcu­ lated from the data in table 1 by the method de­ 25° scribed in earlier sections. The values of pKbh KH,PO. ______obtained from these two series of measurements are 7. 6370±0. 0004 8. 0700± 0. 0009 KH Phenolslllfonate ______8. 5642± . 0004 8. 0755±. 0007 listed in the last column. The values of pKa were H OL ______8. 0766± . 0007 taken as 7.213, 7.19S, and 7.189 for primary phosphate ion at 20°, 25°, and 30° C, respectively 30° [14 , IS] ; and 9.105, 9.053 , and 9.005 for p-phenol­ KH,PO. ______7. 5622± 0. 0008 7. 9355±0. 0017 ion at the same temperatures l15]. The KH Phenolsulfonate ______8. 471O± . 0004 7. 9371 ± . 0009 mean value of pKbh obtained by the earlier method HOL ______7. 9391±. 0010 of Roberts [1] and Harned and Ehlers [3] from the

524 Journal of Research 8.24 ,...------,------,------, Figures 1, 2, and 3 illustrate the change with ionic strength of the apparent value of PJ(bll, denoted - log J( as derived from the t]u'ee cries of measurements. The open circles repre ent points computed from the first ten rows of Lable 2 '"8 8.20 f--~---+------+------1 and the marked circles from the lasL five rows. ..J I The dots represent amine-phenolsulfonaLe mix­ tures and the half-shaded circles mixtures of 8.18 1-----""""--+------+------1 amine and potassium dihydrogen phosphaLe. A value of 1 for a * in eq 15 gave the lower lines of

8.16 L-_____-'- _____--'- _____---' each figure. The phosphate points correspond to o 0.1 0 .2 0.3 al = 3 and a2=5 in the right-hand term of eq 14, IONIC STREN GTH and the phenolsulfonate points were compu ted FIGU RE 1. Determination of ](bh for tris(hydl'oxymethyl)­ with al = 4 and a2 = 10. The apparent J(b/i was amino methane at 20° C. obtained by the following formula from the Dots, hydrolysis of amine·pbenolsu][onate mixtures; haH·shaded circles, b ydrolysis of am in c-phosph ate mix tures; open ci rcl es and marked circles, apparent values of the m ean given by eq 6 with amille-Hel mixtures. substitution of the right-hand m ember of eq 14 8.09 . ... for the activity-coefficient term: 0 (16) 8.07 ~ The agreement between the thJ'ee determina­ -", tion of PJ(bl. is satisfactory, in view of the de­ 8 8.05 \ ..J pendence of the results furnished by the emf­ I hydrolysis method upon J(a values from other 8.03 \ independent investigations. This procedure gives ~\ promise of usefulness in other studies of basic dissociation. 8.01 A summary of the average values of P[{blt and o 0.1 0.2 0.3 ION IC STRENGTH J(bh and of P[{b and [{b is given i.n Lable 4. For a

FIGURE 2. Determination of ]( bh Jor tris(hydroxymethyl)­ calculation of the basic constant, J(b (wh ich eq uals aminomethane at 25° C. J(W/[{bh) , p[{w was taken to be 14.167 at 20 °, Dots, hydrolysis of aminc·pbellolsuHonate mi xtures; haH·shaded ci rcles, 13.996 a,t 25 °, and 13.833 at 30° C [19] . The hydrolysis of am ine-phosphate mi xtures; open ci rcles and marked circles, amine-HOI mixtures. value of - log [{b at 25° C (5.920) is to be compared with 5.97 found by Glasstone and Sclu'am [16] 7.9 6 from measurements with the .

7.94 .. TABLE 4. Summary of dissociation constants Jar tl'is­ v - (hydl'oxymethyl) amino methane 0 -", 0\ 0 Temperature I J(bhX 10' § 7.9 2 ------1----:------°C 20 ...... 8. 221 6.00 5.946 1. 133 7 .9 0 \ 25 ...... 8.076 8. '10 5.920 1. 202 \ 30 ...... 7. 937 11. 55 5.89G 1.272 7 .88 o 0.1 0 .2 0.3 V. References IONIC STRENGTH [1] E. J. Roberts, J. Am. Chern. Soc. 52, 3877 (1930). FIGURE 3. Determination of ]( bh Jar t1'is(hydl'oxymethyl)­ [2] H. S. Harned and B. B. Owen, J . Am. Chem. Soc. 52, amino methane at 30° C. 5079 (1930). Dots, hydrolysis of a minc·phenolsulfonate mixtures; haH·sbaded circles, bydrolysis of amine·phosphate mixtUies; open circles and marked circles, [3] H. S. Harned and R. W. Ehlers, J. Am. Chern. Soc. amine·HCI mixtures. 54, 1350 (1932).

Dissociation Constants of Bases 525

,__ [4] R. G. Bates and G. D. Pinching, J. Research NBS [1 5] R. G. Bates, G. L. Siegel, and S. F. Acree, J . Re­ 42, 419 (1949) RP1982. search NBS 31, 205 (1943) RP1559. [5] E. J. Roberts, J . Am. Chem. Soc. 56, 878 (1934). [16] S. Olasstone and A. F. Schram, J. Am. Chem. Soc. [6] B. B. Owen, J . Am. Chem. Soc. 56, 2785 (1934), 69, 1213 (1947). [7] E. W. Kanning and A. F. Schmelzle, Proc. I ndiana [17] G. D. Pinching and R. O. Bates, J . Research NBS Acad. Sci. 51, 150 (1941) . 37, 311 (1946) RP1749. [8] R. G. Bates, Chem. Rev. 42, 1 (1948). [9] T. M. Lowry, J. Soc. Chem. 'Ind. "'2, 43 (1923). [18] R. G. Bates and S. F. Acree, J . Research NBS 30, [10] J . N. Brpnsted, Rec. trav. chim. 4:2,718 (1923), 129 (1943) RP1524. [11] R. O. Griffith, Tra ns. Faraday Soc. 17, 525 (1922). [19] H. S. Harned a nd B. B. Owen, The physical chemistry [12] R. G. Bates, J. Am. Chem. Soc. 70, 1579 (1948). of electrolytic solutions, p. 485. (Reinhold Pub­ [13] G. G. Manov, R. O. Bates, VV. J . Hamer, and S. F. lishing Corp., New York, N. Y. 1943.) Acree, J . Am. Chem. Soc. 65, 1765 (1943). [14] R. G. Bates a nd S. F. Acree, J. Research NBS 3"', 373 (1945) RP1648. WASHINGTON, July 15, 1949.

526 Journal of Research